Question

The HSB club is selling HSB hoodies. Hoodies cost the club $10 each. One member suggests marking them up 50% and charging $15. Another points out that hoodies generally sell for $13. Another student suggests that students may want one for sentimental reasons, and thinks the price elastic of demand is fairly low, say 2. If that’s the case, what would be the price of an HSB hoodie?

Drawing from the answer a new member of HSB suggests that the club raise the price from $20 to $25. How many hoodies must the club sell to be at least as well off as at the lower price?

Answer 1

A. The find the price (either 13 or 15), we must find out which one will give us higher revenue. And we know that

Revenue=Quantity Demanded*Price.

It is given that the price elasticity is 2. We also know that

Price elasticity of demand= %change in dmeand/% change in price.

Now, letsy say x number of hoodies will sell at a price of 13, this means

Revenue at price if 13= 13x.

If the price is increased to 15,

%change in price= (15-13)/15=2/15=13.33%.

Using the PED equation

2=%change in demand/13.33%

%change in demand=2*13.33%=26.67%.

So demand will drop by 26.67%. This means the revenue at price 15 would be

15*(1-.267)x

=15*.733x

=11x

Since revenue at price 13 (13x) is higher than revenue at price 15 (11x), the price would be 13.

B. To be as well off means to have the same revenue. Lets say that y hoodies were being sold at price 20. This means

Revenue at price 20= 20y.

The new price is 25. If z hoodies get sold at this price

Revenue at price 25=25z.

Equating, to be as well off as before

20y=25z

4y=5z

z=.8y

It means at least 80% of the previous amount of hoodies must be sold to be as well off.